Joint dynamic pricing and marketing-mix strategies for revenue management applications with stochastic demand

To attract potential customers and to effectively sell their inventories over time, retailers often invest in different marketing levers and apply dynamic pricing strategies. However, composing a profitable marketing mix in dynamic settings is challenging. The high problem complexity increases further if one seeks to account for stochastic and inventory-dependent demand, which is essential for various practical applications. In this paper, we examine such stochastic dynamic pricing and marketing models under a finite as well as an infinite time horizon. We assume that marketing dimensions, such as information advertising, design quality, and the like, are substitutes only if they are all positive; otherwise, the demand vanishes. For a reasonably general demand formulation with asymmetric multidimensions marketing, we show how to transform the multidimensional optimal control problem into a two-dimensional one, simplifying the analytical complexity. Further, for well-established cases with isoelastic and exponential demand, we present optimal closed-form solutions allowing detailed sensitivity analyses. Using numerical examples, we illustrate and analyze how optimally controlled sales processes are influenced by different model parameters and infer managerial insights. Our results provide general qualitative and quantitative insights into the complex interplay of marketing-mix controls over time.